1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$$ are coplanar if :
A
$$k=3$$ or $$-2$$
B
$$k=0$$ or $$-1$$
C
$$k=1$$ or $$-1$$
D
$$k=0$$ or $$-3$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
$$\overrightarrow a \,,\overrightarrow b \,,\overrightarrow c $$ are $$3$$ vectors, such that

$$\overrightarrow a + \overrightarrow b + \overrightarrow c = 0$$ , $$\left| {\overrightarrow a } \right| = 1\,\,\,\left| {\overrightarrow b } \right| = 2,\,\,\,\left| {\overrightarrow c } \right| = 3,$$,

then $${\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a }$$ is equal to :
A
$$1$$
B
$$0$$
C
$$-7$$
D
$$7$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The radius of the circle in which the sphere

$${x^2} + {y^2} + {z^2} + 2x - 2y - 4z - 19 = 0$$ is cut by the plane

$$x+2y+2z+7=0$$ is
A
$$4$$
B
$$1$$
C
$$2$$
D
$$3$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
A tetrahedron has vertices at $$O(0,0,0), A(1,2,1) B(2,1,3)$$ and $$C(-1,1,2).$$ Then the angle between the faces $$OAB$$ and $$ABC$$ will be :
A
$${90^ \circ }$$
B
$${\cos ^{ - 1}}\left( {{{19} \over {35}}} \right)$$
C
$${\cos ^{ - 1}}\left( {{{17} \over {31}}} \right)$$
D
$${30^ \circ }$$
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